t h to f p - tcm.phy.cam.ac.ukachc2/written/lec5b.pdf · 2 ni d ard tidy x o low length rule wtoff...
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Continuoussymmetry breaking
and Goldstonemodes
T T H K H to F P
Ginzburg LondonHamiltonian fr n 2
p Had fddx t ni tum t E IE mT b in
it For b pHhas fullglobalrotationsymmetry
in Yin space
but ground state is ferromagnetic
I e At TeTa appearance of longrangeorder
and is accompaniedby spontaneous symmetrybeating
ii Uniform Cie global spinrotations wit no
energy but requiresmotiveofwholesystem
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A story varyyCin yea rotation into
mylittle energyform low energy
collectiveexutates
e.g magners shinbonesphonons
orI
PA
longitudetown
yspheremode amplitudemods
are Marniemx int
energymy
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Grundythe breathing of a
continuoussymmetry
existenceof low energy
excitation
Goldstonemods
Goldstonemods have a dramatic influence on the
nature ofLro in ten dimensions
see this unit h 2 XY yes superftweb
Zz Hy ne I
T r r p Itdomainhalls
T CTe T
JIm it o
a.m in tis go
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pHCOT p It t KIfth lgotI k
3 Doc epHCo
looks Gansin ht niteOCD is fainter 21
th mas ther are contraint an or enhgf
and this admit topologically non timid
field configurtsvortices
chpproximhi fr large To lieten T we assure
that the untruth In Zis small
tu d 2
0 is unconstrained
o o
L O ly OKs G y I Cdcx X
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whe Fedex SdCx Coulomb pathsin d denim
Applying fans der
Goldindeux dotx IcdI SdXt dydxtsurfeau of a unitd diment bull
Sd 2got
TCE
dadIqni
d
2 dCd I
G d Sdt cont
Sr L oh 06557 2 Coto co 06,7
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2 ni d ar d
Tidyx o low length
rule wt offoCx ocos I lost d 2 x o
ly div d 2drips de 2
WB denims d 32 the apps a short
byth rule or UV diverges In principle this
wld be controlledby modifyingthe Henthorn
at short length rub lattice regularisation
Hour since we knowtht this is an
implicit lathesent we knewthe diverges
is
unplyrid so we can neglect it
tonsequiesm D in reCeiLOCH deo.Dy
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in expf I do ex oath
x
hi dazo de2
True Leo shouldapproach a file content
tf Jew fluctuates destoyd Lro
Mermin Waywthorn
Fer system withcontinuous
symmetry Cad
shot rangedinteraction then is he Lro in
denims da fo ay finitetemperature
That fluctuates duty Lno
D 2 is hmm as low critical demeim
fr disunitesymmetry low wilddenimD
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Furillo Derivationof Sd
Volume and
Safe era S Sart
f dye Tide dr sandier
An f dt E't
Tik Sd If E
See2
ME
1et r
g drrd Er'stfft dear dr
If E rd 2 1 1